01 stack 20160908_jintaek_seo

StackStack
Mobile Game ProgrammingMobile Game Programming
jintaeks@gmail.com
Division of Digital Contents, Dongseo Univ.
September 8, 2016

Presentation Outline
 ADT
 Data Structure
 Stack
 Implementation of a stack
– KStack
– template KStack
 Algorithms with stack
– Base conversion of numeral system
– Evaluation of postfix notation
– Conversion from infix to postfix notation
2

Abstract Data Type(ADT)
 an abstract data type ( ADT) is a mathematical model for
data types where a data type is defined by its behavior
(semantics) from the point of view of a user of the
data.
 possible values, possible operations on data of this
type, and the behavior of these operations.
 Example: integers
– Values …, -2, -1, 0, 1, 2, …
– Operations
• Addition
• Subtraction
• Multiplication
• Division
• Greater than, etc…
3

ADT examples
 Some common ADTs, which have proved useful in a great
variety of applications, are:
– Container, List, Set, Multiset
– Map, Multimap, Graph, Stack
– Queue, Priority queue
– Double-ended queue
– Double-ended priority queue
4

Data Structure(s)
 a data structure is a particular way of organizing data in
a computer so that it can be used efficiently.
 Data Structures implement one or more particular
abstract data types (ADT).
 Data Structure is a concrete implementation of the
contract provided by an ADT.
 Examples:
– Array, Stack, List
– Associative array, Record(struct)
– Union
– Set
– Graph, Tree
– Class
– …
5

Stack
 an abstract data type that serves as a collection of
elements.
 two principal operations:
– push, which adds an element to the collection.
– pop, which removes the most recently added element that was
not yet removed.
 LIFO (for last in, first out)
 the push and pop operations occur only at one end of
the structure, referred to as the top of the stack.
 may be implemented to have a bounded capacity.
 Overflow
– when the stack is full and does not contain enough space to
accept an entity to be pushed.
6

Stack runtime
 Simple representation of a stack runtime.
7

Hardware stacks
#include "stdafx.h"
void Test( int i )
{
i = 4;
}
void main()
{
int i;
int j;
i = 3;
j = i;
Test( i );
printf( "%drn", i );
}
8

Stack Settings in Visual Studio 2013
 Property pageLinkerSystemStack Reserve Size
9

Working Example
#include <stdio.h>
void Swap(int a, int b) {
int t=a;
a=b;
b=t;
}//Swap
void main() {
int a=2;
int b=3;
Swap(a,b);
printf("%d,%dn",a,b);
}//main
10

#include <stdio.h>
int t=a;
a=b;
b=t;
}//Swap
void main() {
int a=2;
int b=3;
Swap(a,b);
}//main
11

#include <stdio.h>
int t=a;
a=b;
b=t;
}//Swap
void main() {
int a=2;
int b=3;
Swap(a,b);
}//main
12

#include <stdio.h>
int t=a;
a=b;
b=t;
}//Swap
void main() {
int a=2;
int b=3;
Swap(a,b);
}//main
13

Revised working example
#include <stdio.h>
void Swap(int *a,int *b) {
int t=*a;//assigns the contents of a to t
*a=*b;//assigns the contents of b to the location of contents of
a.
*b=t;//assigns the t to the location of contents of b
}//Swap
void main() {
int a=2,b=3;
Swap(&a,&b);//pass addresses of a and b
}//main
14

15
#include <stdio.h>
a.
}//Swap
void main() {
int a=2,b=3;
}//main

16
#include <stdio.h>
a.
}//Swap
void main() {
int a=2,b=3;
}//main

17
#include <stdio.h>
a.
}//Swap
void main() {
int a=2,b=3;
}//main

18
#include <stdio.h>
a.
}//Swap
void main() {
int a=2,b=3;
}//main

C++ implementations of a stack
class KStack
{
public:
KStack() : m_sp( 0 )
{
}
void Push( int data_ );
bool Pop( int& outData_ );
bool IsEmpty() const;
private:
int m_sp;
int m_data[ 100 ];
};//class KStack
19

void KStack::Push( int data_ )
{
m_data[ m_sp ] = data_;
m_sp += 1;
}
bool KStack::Pop( int& outData_ )
{
if( m_sp <= 0 ) return false;
m_sp -= 1;
outData_ = m_data[ m_sp ];
return true;
}
bool KStack::IsEmpty() const
{
return m_sp == 0;
}20

Template KStack
template<typename T, int STACK_SIZE>
class KStack
{
public:
KStack() : m_sp( 0 )
{
}
void Push( T data_ );
bool Pop( T& outData_ );
bool IsEmpty() const;
private:
int m_sp;
T m_data[ STACK_SIZE ];
};//class KStack
21

void KStack<T,STACK_SIZE>::Push( T data_ )
{
m_data[ m_sp ] = data_;
m_sp += 1;
}
bool KStack<T, STACK_SIZE>::Pop( T& outData_ )
{
if( m_sp <= 0 ) return false;
m_sp -= 1;
outData_ = m_data[ m_sp ];
return true;
}
22

void main()
{
KStack<int,100> s;
s.Push( 3 );
s.Push( 5 );
int data;
const bool bIsPop = s.Pop( data );
printf( "%drn", data );
}
23

Actual usage of stack in C++
 std::stack
template<
class T,
class Container = std::deque<T>
> class stack;
 a container adapter that gives the programmer the
functionality of a stack - specifically, a LIFO (last-
in, first-out) data structure.
24

#include <stack>
void main()
{
std::stack<int> s;
int n;
printf( "Enter decimal digit:" );
scanf( "%d", &n );
while( n >= 5 )
{
s.push( n % 5 );
n /= 5;
}//while
25
printf( "Equivalent Quintett
is %d", n );
while( s.empty() == false )
{
n = s.top();
printf( "%d", n );
s.pop();
}//while
}//main

Algorithms with Stack
 Convert Decimal Number to Pentamal Number
 Reverse Polish Notation: Evaluating Postfix Notation
 Conversion from Infix to Postfix Notation
26

Convert Decimal Number to Pentamal Number
 divide the number by 5.
 write quotient and remainder.
 now quotient is dividend, continue till dividend is
less than 5.
27

void main()
{
KStack<int, 100> s;
int n;
printf( "Enter decimal number:" );
scanf( "%d", &n );
while( n >= 5 )
{
s.Push( n % 5 );
n /= 5;
}//while
printf( "Equivalent pentamal is ", n );
while( s.Pop( n ) )
printf( "%d", n );
}//main28

Practice
 Write a class that convert decimal number to n-ary
number.
– binary
– trimal
– tetramal
– pentamal
– hexamal
– heptamal
– octal
– nonamal
 there must a getter that gets the converted number in
string.
29

Reverse Polish Notation: Postfix Notation
 the operators follow their operands;
 for instance, to add 3 and 4, one would write "3 4 +"
rather than "3 + 4".
 "3 4 + 5“−  "3 4 5 +"−
– if there are multiple operations, the operator is given
immediately after its second operand.
 it removes the need for parentheses that are required
by infix.
 "3 (4 × 5)“ is quite different from "(3 4) × 5".− −
 In postfix, it could be written "3 4 5 × ", which−
unambiguously means "3 (4 5 ×) " which reduces to "3−
20 “.−
30

Evaluation postfix expression
 While there are input tokens left
– Read the next token from input.
– If the token is a value
• Push it onto the stack.
– Otherwise, the token is an operator (operator here includes
both operators and functions).
• It is known a priori that the operator takes n arguments.
• If there are fewer than n values on the stack
– (Error) The user has not input sufficient values in the expression.
• Else, Pop the top n values from the stack.
• Evaluate the operator, with the values as arguments.
• Push the returned results, if any, back onto the stack.
 If there is only one value in the stack
– That value is the result of the calculation.
 Otherwise, there are more values in the stack
– (Error) The user input has too many values.
31

example: "5 + ((1 + 2) × 4) 3“−  5 1 2 + 4 × + 3 −
32
Input Operation Stack Comment
5 Push 5　
1
Push 1
　
5
2
Push 2
　1
5
+
Add 3
Pop two values (1, 2) and push result (3)
5
4
Push 4
　3
5
×
Multiply 12
Pop two values (3, 4) and push result (12)
5
+ Add 17Pop two values (5, 12) and push result (17)
3
Push value 3
　
17
− Subtract 14Pop two values (17, 3) and push result (14)
　 Result 14

Practice
 Write a class that evaluates a postfix notation.
33

Conversion from Infix to Postfix Notation
While there are tokens to be read:
•Read a token.
•If the token is a number, then add it to the output
queue.
•If the token is an operator, o1, then:
• while there is an operator token o2, at the top of the
operator stack and either
• o1 is left-associative and its precedence is less than or
equal to that of o 2, or
• o1 is right associative, and has precedence less than that of
o2,
• pop o2 off the operator stack, onto the output queue;
• at the end of iteration push o1 onto the operator stack.
•If the token is a left parenthesis (i.e. "("), then push
it onto the stack.34

• If the token is a left parenthesis (i.e. "("), then
push it onto the stack.
• If the token is a right parenthesis (i.e. ")"):
• Until the token at the top of the stack is a left
parenthesis, pop operators off the stack onto the output
queue.
• Pop the left parenthesis from the stack, but not onto the
output queue.
• If the stack runs out without finding a left parenthesis,
then there are mismatched parentheses.
When there are no more tokens to read:
• While there are still operator tokens in the stack:
• If the operator token on the top of the stack is a
parenthesis, then there are mismatched parentheses.
• Pop the operator onto the output queue.
Exit.35

Detailed example: 3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3
 predefined operator properties table.
 How can we implement this properties table?
36

37

38

Practice
 Write a class that converts Infix notation to Postfix
notation.
 Expand the features of existing class(written in
previous learning).
39

int priority( char a ) {
int temp = 0;
if( a == '^' )
temp = 4;
else if( a == '*' || a == '/' )
temp = 3;
else if( a == '+' || a == '-' )
temp = 2;
return temp;
}
int main() {
std::string infix;
infix = "3+4*2/(1-5)^2^3";
std::stack<char> operator_stack;
std::string postfix;
40

for( unsigned i = 0; i < infix.length(); i++ ) {
if( infix[ i ] == '+' || infix[ i ] == '-' || infix[ i ] == '*' || infix[
i ] == '/' ) {
//
} else if( infix[ i ] == '^' ) {
//
} else if( infix[ i ] == '(' ) {
operator_stack.push( infix[ i ] );
} else if( infix[ i ] == ')' ) {
while( operator_stack.top() != '(' ) {
postfix += operator_stack.top();
operator_stack.pop();
}
} else {
postfix += infix[ i ];
}
}
41

if( infix[ i ] == '+' || infix[ i ] == '-' || infix[ i ] == '*' || infix[ i ] == '/'
) {
while( !operator_stack.empty() && priority( infix[ i ] ) <=
priority( operator_stack.top() ) ) {
}
} else if( infix[ i ] == '^' ) {
while( !operator_stack.empty() && priority( infix[ i ] ) <
priority( operator_stack.top() ) ) {
}
} else if( infix[ i ] == '(' ) {
42

while( !operator_stack.empty() ) {
}//while
std::cout << postfix << std::endl;
return 0;
}
43

Actual usage of equation evaluation in C++
 boost::math
 boost::spirit
44

End
 https://en.wikipedia.org/wiki/Abstract_data_type
 https://en.wikipedia.org/wiki/Reverse_Polish_notation
 https://en.wikipedia.org/wiki/Shunting-yard_algorithm
 http://www.cplusplus.com/forum/beginner/16722/
45

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